Toward a general frame semantics for modal many-valued logics
| Autor: | Paula Menchón, Petr Cintula, Carles Noguera |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Current (mathematics) General frames 02 engineering and technology Theoretical Computer Science 020901 industrial engineering & automation Computer Science::Logic in Computer Science Completeness (order theory) 0202 electrical engineering electronic engineering information engineering Finitary General frame Mathematics Discrete mathematics Modal many-valued logics Range (mathematics) TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Modal Mathematical fuzzy logic 020201 artificial intelligence & image processing Kripke semantics Neighborhood frames Geometry and Topology Residuated lattice Software |
| Popis: | Frame semantics, given by Kripke or neighborhood frames, do not give completeness theorems for all modal logics extending, respectively, K and E. Such shortcoming can be overcome by means of general frames, i.e., frames equipped with a collection of admissible sets of worlds (which is the range of possible valuations over such frame). We export this approach from the classical paradigm to modal many-valued logics by defining general $${\varvec{A}}$$A-frames over a given residuated lattice $${\varvec{A}}$$A (i.e., the usual frames with a collection of admissible $${\varvec{A}}$$A-valued sets). We describe in detail the relation between general Kripke and neighborhood $${\varvec{A}}$$A-frames and prove that, if the logic of $${\varvec{A}}$$A is finitary, all extensions of the corresponding logic E of $${\varvec{A}}$$A are complete w.r.t. general neighborhood frames. Our work provides a new approach to the current research trend of generalizing relational semantics for non-classical modal logics to circumvent axiomatization problems. |
| Databáze: | OpenAIRE |
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